Poisson process factorization for mutational signature analysis with genomic covariates

2025-10-29

AI Summary

Existing mutational signature analysis methods—such as non-negative matrix factorization (NMF)—ignore the genomic non-uniformity of somatic mutations and tissue- or locus-specific covariates (e.g., replication timing, histone modifications), limiting their ability to model spatial heterogeneity of mutational processes. To address this, we propose Poisson Process Factorization (PPF), a generalization of NMF into a Poisson regression framework that flexibly incorporates genomic covariates via covariate-dependent intensity functions modeling regional mutation rates. PPF employs a hierarchical sparsity-inducing prior to automatically infer the number of mutational processes. Parameter inference and uncertainty quantification are performed via maximum a posteriori estimation and Markov Chain Monte Carlo sampling. Applied to breast cancer data, PPF uncovers synergistic regulation of mutational processes by copy-number alterations, epigenetic marks, and other genomic features, substantially improving spatial resolution and biological interpretability of mutational signatures.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Mutational signatures are powerful summaries of the mutational processes altering the DNA of cancer cells and are increasingly relevant as biomarkers in personalized treatments. The widespread approach to mutational signature analysis consists of decomposing the matrix of mutation counts from a sample of patients via non-negative matrix factorization (NMF) algorithms. However, by working with aggregate counts, this procedure ignores the non-homogeneous patterns of occurrence of somatic mutations along the genome, as well as the tissue-specific characteristics that notoriously influence their rate of appearance. This gap is primarily due to a lack of adequate methodologies to leverage locus-specific covariates directly in the factorization. In this paper, we address these limitations by introducing a model based on Poisson point processes to infer mutational signatures and their activities as they vary across genomic regions. Using covariate-dependent factorized intensity functions, our Poisson process factorization (PPF) generalizes the baseline NMF model to include regression coefficients that capture the effect of commonly known genomic features on the mutation rates from each latent process. Furthermore, our method relies on sparsity-inducing hierarchical priors to automatically infer the number of active latent factors in the data, avoiding the need to fit multiple models for a range of plausible ranks. We present algorithms to obtain maximum a posteriori estimates and uncertainty quantification via Markov chain Monte Carlo. We test the method on simulated data and on real data from breast cancer, using covariates on alterations in chromosomal copies, histone modifications, cell replication timing, nucleosome positioning, and DNA methylation. Our results shed light on the joint effect that epigenetic marks have on the latent processes at high resolution.

Problem

• Incorporating genomic covariates into mutational signature analysis
• Modeling non-homogeneous mutation patterns across genomic regions
• Automatically inferring active latent factors without multiple fittings

Innovation

• Poisson process factorization with covariate-dependent intensity functions
• Sparsity-inducing priors for automatic latent factor selection
• Bayesian inference via MAP estimation and MCMC uncertainty quantification